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NumericalAlgebraicGeometry :: randomInitialPair

randomInitialPair -- a random initial pair

Synopsis

Description

Generates a start system S that has an equal chance of reaching any of the solutions of the target system T. For more details see: C. Beltran and A. Leykin, "Certified numerical homotopy tracking", arXiv:0911.1783

i1 : T = randomSd {2,3};
i2 : (S,solsS) = randomInitialPair T

                                   2                                    
o2 = ({(- .0887354 - .0393054*ii)x1  + (.527153 + .0470438*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                             2                                               
     .140735 - .0654691*ii)x2  + (- .00601739 - .239146*ii)x1*x3 + (- .261112
     ------------------------------------------------------------------------
                                                    2              
     + .162775*ii)x2*x3 + (- .109756 - .250729*ii)x3 , (- .348669 +
     ------------------------------------------------------------------------
                   3                             2                 
     .0109453*ii)x1  + (- .134995 - .359948*ii)x1 x2 + (- .416105 -
     ------------------------------------------------------------------------
                      2                           3              
     .0893526*ii)x1*x2  + (.225476 + .153456*ii)x2  + (.0349735 -
     ------------------------------------------------------------------------
                  2                                                    
     .293502*ii)x1 x3 + (.000431451 + .0374434*ii)x1*x2*x3 + (.118872 +
     ------------------------------------------------------------------------
                  2                                  2               
     .405281*ii)x2 x3 + (- .548156 - .126004*ii)x1*x3  + (- .210456 -
     ------------------------------------------------------------------------
                      2                              3
     .0600457*ii)x2*x3  + (- .0138736 + .117632*ii)x3 },
     ------------------------------------------------------------------------
     {{-.110109+.486205*ii, .22145-.128357*ii, .827251-.040248*ii}})

o2 : Sequence
i3 : M = track(S,T,solsS,gamma=>0.6+0.8*ii,Software=>M2)

o3 = {{-.192161+.2839*ii, .154087+.1964*ii, .874383-.235824*ii}}

o3 : List

See also

Ways to use randomInitialPair :